Revisiting the Mysterious Mpemba Effect

Transcription

1 Prceedings f the Technical Sessins, 24 (28) R.P.Gamage and S.R.D.Rsa Department f Physics, University f Clmb, Clmb 3 ABSTRACT The effect f ht water freezing faster than cld water is mentined in Greek literature. Hwever, it came ut as a scientific phenmenn during the last few decades and is knwn as Mpemba effect since But there is an inadequacy f explanatin which was a challenge t the mdern science. Hence, it is an imprtant issue t revisit this mysterius effect. In this research wrk it is attempted t justify the Mpemba effect in terms f the heat lss thrugh a number f experiments. A newly intrduced technique was used t explre the influence f evapratin n the effect using a thin il layer. Mrever it was nticed that higher the length f time duratin, greater the chance f bserving the effect. Finally the Mpemba effect is classified int tw, based n cling curves knwn as High Cling Rate (HCR) and Quick Freeze (QF). Then they were analyzed and justified by means f relevant simulatins and lgical interpretatins. Finally it was cncluded that the evapratin and nature f ice due t cnvectin current are the main reasns fr the effect. A new bservatin arund 4 C is als fund in the research. 1. INTRODUCTION 1.1 What is Mpemba Effect The effect f ht water freezing faster than cld water is knwn as Mpemba effect. But this is in adequate as a scientific definitin [1]. There are tw quantities, initial temperature and freezing which are very imprtant t define crrectly because they are the main parameters f the effect. Maximum temperature that reaches in the heating prcess is knwn as initial temperature in these experiments. Every liquid in the freezing prcess absrbs sme heat knwn as latent heat f fusin. Cling curves can be used t identify this event as a straight line. But disslving sme cmpunds in water decreases the freezing pint. Cnsidering the given tw samples f water, if ne f them first reaches zer r depart frm zer after absrbing latent heat, then it can be cnsidered as the first frzen sample. The first ne is respnsible fr high cling rate (HQR 1 ) and the secnd is quick freezing (QF 1 ). But it is difficult t separate these tw since literature examples shw ne f these r bth may happen. Later these tw phenmena will be deeply and separately cnsidered. 1 HCR & QF are first intrduced in this research fr reference purpses.

2 Prceedings f the Technical Sessins, 24 (28) Why is it Mysterius? Nrmally cling f tw bdies is described by Newtn s law f cling (since 1688). Accrding t Newtn s law tw samples f water with the same cnditins take equal time duratin (t) t pass certain temperature range. Althugh time taken fr ht water t reach the temperature f the cld water shuld be lesser (δt), but it cannt be zer and never minus. But first mystery is; t, δ t > t + δ t < t But sme graphs mentined in literature shws that the prblem is arund the freezing pint (QF).secnd mystery is hw the same amunt f water has a different latent heat f fusin. Unlike in ther scientific phenmena, difficulty f reprducing is the third mystery. 2. LITERATURE REVISITING 2.1 Histry The Mpemba effect has lng been knwn in the western wrld due t wintry weather but nt in this name until the previus century. It als mentined by Greek philsphers, medieval physicist and philsphers. In time, a mdern thery f heat was develped, and the earlier bservatins were frgtten. The first tw decades f twentieth century was very imprtant fr physics Especially Bltzmann intrduced the mdern understandings f thermdynamics and Statistical Physics. Hwever, by this time n ne had knwledge n this effect. Mpemba stands fr Tanzanian schl student Erast B. Mpemba. He was a secndary schl student in Tanzania, and fund this effect when he was making ice cream, Mpemba and Osbrne later published their results. In the same year, Dr. Kell f Canada independently reprted the phenmenn, alng with a theretical explanatin. 2.2 Mdern Research and explanatin Mdern researches n this effect are trying t mdel the effect mathematically and investigate it thrugh the gas cncentratin; the research previusly dne in Sri Lanka has investigated the effect thrugh in cncentratin. It is extremely useful t mentin the fllwing currently use suggestins. Evapratin - When initially warmer water lse significant amunts f water thrugh evapratin. The reduced mass will make it easier fr the water t cl and freeze. Evapratin cannt explain experiments which were dne in clsed cntainers, where n mass was lst t evapratin. And many scientists have claimed that evapratin alne is insufficient t explain their results. Other suggestins are disslved gasses, cnvectin, surrundings and supercling.

3 Prceedings f the Technical Sessins, 24 (28) METHODOLOGY 3.1 Temperatures Measuring System The system cntains temperature sensrs (DS18S2), Micrcntrller (PIC 16F877A), PC, SSD display and a Cling ven (Temperature range is -6 C t 8 C). They are arranged as fllws. This system was used precisely fr the research previusly dne in Sri Lanka [4]. Figure 1a: Temperatures measuring system. Figure 1b: Final experiments apparatus. Temperature sensr (DS18S2) has.5 C accuracy. Then the cllected data pint has ±.5 C accuracy but cling curves have been gne thrugh interplatin prcess t have a smth nature using MATLAB smth( ) cmmand. 3.2 Pssible Experiments There are lts f experiments t investigate this but it is imprtant t mentin that these experiments are based n in cnsecratin rather than heat lss. Mrever, an experiment with an il layer is first intrduced in this experiment. It is reliable an accurate than the experiment in clsed cntainer, since in a cntainer with a lid it is difficult t say that it des nt absrb the energy f evaprated mlecules but here evapratin never ccurs. But it des nt cmpletely remve the heat lss frm the surface. Then it is reasnable t assume that this trick mainly halts evapratin. And il layer des nt change the uter pressure as well. 3.3 Scientific Path f the Methd Scientific methd wuld be applied in tw ways fr this experiment. If effect can be fund, then try t reduce the effect by changing sme parameters. The prgress f this reductin is respnsible fr dependency n the changed parameter. If the effect cannt be fund, then the path will get the cunter way with the same argument. One example is given here. Ex: - Oil layer experiment:-effect can be fund: - Oil layer insert n the ht water. Effect cannt be fund: - Oil layer insert n the cl water.

4 Prceedings f the Technical Sessins, 24 (28) NEW HYPOTHESIS 4.1 Evapratin Based Mdel Dr. Kell f Canada gave the explanatin based n evapratin.that explanatin has tw main prblems, mass lss is nt enugh t explain the effect and smetimes experiment with a clsed cntainer shws the effect. But we knw that evapratin is a randm prcess and als in this prcess particles with high energy are lst. Then the prbability f chsing an escaping practical frm the left f the Gaussian distributin is high. Then new calculatin shuld be mdified as belw. E = m c Tdt, c = evprative heat capacity ( c >> c & c α T ) cling curve e e e e The new heat capacity intrduced here is a functin f temperature. It is the energy lst frm certain amunt f liquid t reduce its temperature by 1 C due t evapratin and ther prcesses such as cnductin, cnvectin and radiatin. But evapratin can be applied nly fr liquid and it s the predminate factr fr liquids. It is knwn as evaprative heat capacity. As further suggestins, ht water cntinues the cnvectin current after 4 C because ht water has high speed particles than cld water which helps t freeze. This phenmenn has very chatic nature that may be respnsible fr randmness. Ht water mlecules may have higher rtatinal mtin which may increase the prbability fr cnnecting the mlecules fr freezing prcess. 5. EXPERIMENT RESULTS I When we are studying these data (graphs) it is imprtant t bserve bth events cnsidered in sectin 1.1 i.e. QF & HCR.This sectin cntains the experiments which are directed t find ut depending parameters f the effect and distilled water was used fr experiments t avid in cncentratin, but it was unable t shw the effect even with carbnated water. 5.1 Time Measurements. This sectin cntains time measurement f the cling curve. Objectives f this analysis were t find ut the dminant phenmena frm the tw previusly intrduced effects (QF, HQR) and identify the initial temperatures which shw effect clearly. Fllwing three time perids were measured frm the cling curve t achieve abve bjectives. Time taken t reach initial temperature t C - Cling time Time taken frm initial temperature t end f freezing - Freezing time Time taken t absrb latent heat Figure 2 shws the cling times fr all distilled water samples. The curve fitting t these data is dne by neglecting exceptinal values. Then shape f the fitting shws the effect fr

5 Prceedings f the Technical Sessins, 24 (28) high cling rate (HCR). Fr an example if we cnsider 55 C and 75 C the effect is there but it is difficult t bserve (~6s).Equatin f this fit is Time = x + x + Eq x = initial Temperature, ( 5.1) 55 C s,75 C s Time (s) Time vs. Initial Temperature Initial Temperature (`C) Figure 2: Cling time vs. initial temperature 5.2 Current Observatins and Planning Next Experiments Randmness f effect and difficulty f repeating were the main bservatins, High cling rate cannt be clearly bserved but sme samples f water has shwn lw latent heat. Althugh carbnated cl water shuld increase the effect as current suggestins it is same as distilled water hwever Carbnated water has made sft ice., Oil layer has an influence n cling but nt enugh t give the effect, Then experiments are dne with different cling rates and nrmal water until the effect f high cling rate is bserved. The literature als shws the randmness f this effect [2]. 6. EXPERIMENT RESULTS II As mentined in previus sectin we used nrmal water but here the ambient temperature was gradually increased fr experiments. Experiments were very time cnsuming hwever it was pssible t find the effect at ambient temperature -2 C. 6.1 Experiments at -2 C Ambient Temperature. This was the first time where the HCR culd be bserved and here it shws the lw latent heat as well. Repeating f abve experiment als gave the same results. A dted line shwn in next graph is respnsible fr il layer n ht water which has remved HCR. Temperature (`C) 8 Cling Curves Temperature (`C) 7 Cling Curves Time (s) Time (s) Figure 3a: Experiment at -2C ambient temperature Figure 3b: At -2 C Repeating and il layer

6 Prceedings f the Technical Sessins, 24 (28) Thereafter the results are verified t ceramic cntainer as well. Variables f the curve Cling Time vs. Temperature at -2 C Freezing Time (- 35 C & -2 C) Fitted equatin and time Deference 2 Time = x-.6476x ( Eq 7.1) x = Initial Temperature, then, 72 C s,54.5 C s t = s 2 min 2 Time = x-.64x ( Eq 7.3) x = Initial Temperature, then 72 C 3776 s,55 C 462.4s t = 286.4s 5min 6.2 Time taken t absrb latten heat (-35 C & -2 C) Time taken t absrb latent heat vs. initial temperature was pltted fr bth -35 C and - 2 C t identify the differences in the latent heat with the initial temperature. Highest curvature was fund ad -35 C Time (s) 7 65 Time vs. Initial Temperature Temperature (`C) Cling Curves Initial Temperature (`C) Time (s) 4 Figure 4: Observatins 6.3 Observatins Pssibility f repeating is high fr this ambient temperature (-2 C),high cling rate (HCR) can be bserved, sme samples f water shw lw latent heat, carbnated water makes sft ice, il layer has an influence n cling and remve the effect, bservatins can clearly be dne with cnsiderable time difference, the cntainer has n cnsiderable influence. 6.4 Special Observatin This sectin includes a special bservatin, which seems t be related with the effect. In all cling curves a small distrtin is bserved n the 4 C line. This is a special bservatin which can be related with ther suggestins in sectin 4 as well.

7 Prceedings f the Technical Sessins, 24 (28) NEW EXPLANATIONS 7.1 Develpment f evapratin based mdel Suggestins in sectin 4 and results f the il layer experiment shws evapratin is the main reasn fr the effect. This mdel suggests that a small mass lss can remve higher amunt f energy frm water because the particles are remved frm the left f the Gaussian distributin. Temperature 7 (`C) 6 Cling curves Cnsider Only evapratin Time (s) Figure 5a: Remving particles frm a left f Gaussian distributin. Figure 5b: Results f the simulatin. Then a cmputer simulatin was written accrding t equatin 2E T = t exhibit this using the Mntical methds. 3 2E E = kt T = T α E, k = Bltsman ' s cnstent 2 3k Steps f the cmputer simulatin are as fllw 3k STEP Generate tw sets f randm numbers having thusand randm numbers each. Set the mean as 7 and 5 by multiplying the set by 7 and 5.Ordering them in ascending rder and put them in t an array (array1). Remve last number. Get the new mean and put in t new array Repeat last tw steps several times & Plt arry2 RESPONSIBLE PHYSICAL PHINOMINA Temperature distributin f particles Cl and ht water sample Evaprate particle with high energy New temperature Cling curve nly with nly cnsidering evapratin The result are shwn in Figure 5, Ht water curve has the highest slpe. But the fact that this is a randm prcess and will nt happen always is useful t explain the effect. Thereafter cmbining this with Newtn s law f cling will help t explain the effect.

8 Prceedings f the Technical Sessins, 24 (28) CONCLUSION AND DISCUSSION 8.1 Cnclusin Results were helpful t draw the fllwing cnclusins; The Mpemba effect can be classified int tw, HCR and QF. The fact that ht water freezes sn is a cnsequence f thse tw events. Evapratin is the main reasn fr HCR. The nature f ice is the main reasn fr QF. Ambient temperature is imprtant t bserve effect. Equatins f fitted curve give tw temperature values where the effect ccurs. But still generalizatin f thse equatins is needed; that is fr any cntainer, any ambient temperature and fr any amunt f water etc. 8.2 Discussin Sectin 8 gives the explanatin t bservatin except fr hw the ambient temperature influences the effect. But it can be described as fllws. Cnsider the fllwing questin. Wh will win the match between great sprint athlete and the nrmal yung man? With the cmmn sense, the answer is sprint athlete but that is when we cnsider a shrt distance. But what happen when the questin is abut twenty kilmeter race. Nw sprint athlete may nt be the exact answer. This means that the expected results are nly achieved in small space r small time. That is why the effect is bserved mre times when the ambient temperature is increased since it gives a lnger time fr the prcess. This is the main reasn fr the difference between sectin 6 and 7. Using 5ml f water at ambient temperature -2 C will give 1 hur difference (sectin 7.6:12x5=1 hur) in time as Mpemba bserved. Then it seems imprtant t turn twards the thermdynamic explanatin than the in cncentratin r mlecular base appraches. As a future develpment fitted curve shuld be crrected fr lw temperatures as well and experiment shuld be carried ut with lw ambient temperature. REFERENCES 1. MONWHEA JENG Ht water can freeze faster than cld Department f Physics, Suthern Illinis University Edwardsville, Edwardsville (25). 2. MATH FREEZING TEAM, Mdeling the Mpemba Effect, university f Delaware (24). 3. KATZ J. I, When ht water freezes befre cld, Department f Physics and McDnnell Center fr the Space Sciences Washingtn University, St. Luis (26). 4. VITHANAGE C.U, FERNANDO I.M.K and EDIRISINGHE M, Study f Mpemba effect?, Department f Physics, university f Clmb, Sri Lanka (25).